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https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events
Recent Events in en-usMon, 24 Oct 2022 07:46:16 PDT3600Tensor Eigenvalue Problems and Modern Medical Imaging
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/8
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/8Thu, 20 Feb 2020 12:35:00 PST
Tensors (or hypermatrices) are multidimensional generalization of matrices. Although historically they are studied from the perspective of combinatorics and (hyper)graph theory, recent progress in the subject shows how useful they are in more applied sciences such as physics and medicine. In this presentation, I introduce a few tensor eigenvalue problems and their application to higher order diffusion tensor imaging such as diffusion-weighted magnetic resonance imaging (DW-MRI) and higher angular resolution diffusion imaging (HARDI).
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Vehbi Emrah PaksoyUsing Slow-Fast Dynamical Systems to Understand Regime Shifts in Ecology
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/7
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/7Fri, 04 Oct 2019 12:05:00 PDT
In ecology, regime shifts are continual rapid change between different long-lasting dynamics. For instance, rapid evolutionary changes have been observed in a wide variety of organisms, both in predators and in prey. Another example is disease outbreak, where a system exhibits qualitative changes after long periods of apparent quiescence. Using the theory of slow-fast dynamics, for systems of differential equations with sufficiently large separation of time scales we derive conditions under which regime shifts occur. This is joint work with Shigui Ruan and Gail Wolkowicz.
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Ting-Hao HsuAlgebraic Frames and Ultrafilters
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/6
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/6Fri, 01 Nov 2019 12:05:00 PDT
A frame, also known as pointfree topology, is a complete lattice that satisfies a strong distributive property, known as the 'frame law.' Originally, the study of frames began as studying topological spaces without points, hence the name pointfree topology. Due to this connection, different topological concepts can be generalized to frames, for example, compactness. In the first part of the talk, I will explain the basic notions of frames and their connection with topology. It turns out that we can find frame structure in other categories than topological spaces. For example, given a commutative ring R with identity, the lattice of radical ideals of R, Rad(R), is a frame. As a result, concepts from ring structure can also be generalized to frames, for example, primes and minimal primes, annihilators, etc. I will discuss some of these concepts in the language of frame theory. In the last part of the talk, I will describe filters and ultrafilters on frames and show their connections with certain prime structures of a frame.
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Papiya BhattacharjeeHow Mathematics Can Help Winning the War Against Cancer?
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/5
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/5Fri, 18 Oct 2019 12:05:00 PDT
In this talk, I will present a few mathematical models that aims to understand how our immune system interact with cancer cells. In particular, we focus on a model that studies the role or regulatory T cells. Recent advance in the field of regulatory T cell reveals that it plays a vital role during immunotherapy. For example, a higher ratio between regulatory T cells and effector T cells within tumor tissue is associated with worse prognoses in many cancers, including ovarian cancer (Leffers et al., 2009), lung cancer (Tao et al., 2012), glioblastoma (Sayour et al., 2015). On the other hand, the tug war between regulatory T cells and effector T cells for interleukin-2 may chisel immune response against cancer. In this talk, we demonstrate mathematically, for the first time, that the initial ratio between regulatory T cells and effector T cells does impact the tumor recurrence time. We also demonstrate the effectiveness of utilization of IL-2 may flip the outcome of immunotherapy, providing further evidence that it may be clinically viable to modulate the consumption of IL-2 by Tregs.
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Peng FengSoccer Tournament Matrices
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/4
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/4Thu, 30 Jan 2020 12:35:00 PST
In this talk, I will present a combinatorial object, soccer tournament matrices, which is understandable to undergraduate students and gives a taste of combinatorial matrix theory. Consider a round-robin tournament of n teams in which each team plays every other team exactly once and where ties are allowed. A team scores 3 points for a win, 1 point for a tie, and 0 point for a loss, then each particular result leads to a soccer tournament matrix. Let T(R, 3) denote the class of all soccer tournament matrices with the row sum vector R. In this talk, I will explore some necessary conditions of a vector R, such that T(R, 3) is nonempty with the audience, and then for some R, I will show an algorithm to construct a soccer tournament matrix whose row sum is R.
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Lei CaoMinimal Rank Completions of Partial Matrices
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/3
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/3Fri, 15 Nov 2019 12:00:00 PST
Completion problems for partial matrices are defined and partial matrices are associated to bipartite graphs. Minimal ranks for scalar and block partial matrices with simple structures are presented. Calculating the minimal rank is classified as an NP-hard problem, what means that in general it is very difficult to calculate the minimal rank of a unstructured block (scalar) partial matrix. A conjecture states that the minimal rank of a partial matrix has an exact formula if and only if the associated bipartite graph is chordal. We present some upper estimates for the case that the associated bipartite graph is a single cycle, the most simple non-chordal case. The symmetric cyclic case is also treated.
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Edgar PereiraHow Good Are Standard Copulas Anyway?
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/2
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/2Thu, 07 Nov 2019 12:25:00 PST
First, we will raise a question: How good are standard copulas in capturing the dependency structure? To this end we will offer a series of simulated/numerical examples demonstrating that, more often than not, standard model copulas do not capture the underlying dependency structure. We believe that copula models, unlike other statistical tools, are too readily accepted by practitioners. Rigorous, goodness-of-fit tests are commonly replaced by off-hand statements like: “it works well”. To this end, the second part of the talk offers a theoretical result, an umbrella type theorem tailored for creating numerous Goodness of Fit tests for copulas.
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Dragan RadulovicEigenvalue inequalities of matrix product
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/1
https://nsuworks.nova.edu/mathematics_colloquium/ay_2019-2020/events/1Fri, 20 Sep 2019 12:05:00 PDT
Given two n-by-n complex matrices, one is Hermitian and one is positive semidefinite, all of the n eigenvalues (counting multiplicities) of the product of the given matrices are necessarily real. Selecting any k of the n eigenvalues, we present lower and upper bounds for the sum of these k selected eigenvalues. Our results extend and complement the existing ones.
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Fuzhen Zhang